22 



C. V. L. Chaiiier. 



seeutive days. Tlius on the T"", 8"' and 9"" August there occurred in all 11 cases 

 of typhoid fever, on the 10^'', 11"' and 12"' in all 24 cases a, s. o. 



Date Aug. 5, 8, 11, 14, 17, 20, 23, 26, 29, Sept. 1, 4, 7. 



Frequency 2, 11, 24, 49, 46, 32, 16, 23, 10, 5, 2, 0.5. 

 Class —6, -5, —4, —3, —2, —1, 0, +1, -f2, -f-3, -f4, +5. 



Hence the class range is equal to 3 days. The provisional origin was taken 

 at the 23"' August. 



For the parameters of the theoretical frequency curve I obtained the values 





220.5, 



b = 



— 1.658, 



a = 



+ 2.0,58, 



ß3 = 



— 0.0882 





— 0.0017 



The mean corresponds to the date Aug. 18.0, the standard deviation amounts 

 to 6.17 days. The comparison between theory and observation is shown from 

 f]g. 12. The discrepancies are here rather great, as may be expected from such 

 material. It is obviously connected with great difficulties to determine with some 

 certainty the beginning of the disease in each individual case. Probably accuracy 

 may be augmented if the attention of the physicians is directed to the importance 

 of accurate statistical determinations. 



Notwithstanding the imperfection of the material, we find that the theoretical 

 frequency curve reproduces the general features of the curve indicated by the 

 observations fairly well. The negative skewness implies that the increase in the 

 number of infected persons is more rapid than the subsequent decrease after the 

 maximum is reached. This is perhaps characteristic for all such fever maladies. 



IV. Type B of frequency curves. 



This type is expressed by means of the generating function 



(10) 



sni Tzx 



+ 



l{x—l) ' \2(x — 2) \S{x — 3) 



+ . . . 



We write '^-^ {x), for ']j (,/;), if we want to indicate that a parameter X occurs in 

 '^(x). We find from (10) that '\){x) is a ivJwle transcendent function of x, which hence 

 is infinite for no finite value of x. For x =^ — 1, — 2, — 3, ... '!^{x) vanishes. 

 Considering 'l>'^{x) as a function of X, we also find that this function is a whole 

 transcendent function of X. I have given (»Meddelanden» N:o 26) for ']> (;r) also 

 another form, as an integral, namely 



